{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We've been trying to use the analytical (Buckley-Leverett) solution of the two-phase flow in porous media to fit the Corey-type relative permeability model to the experimental oil recovery data. In this post, I'm going to compare the numerical solution of the same model with the analytical results. You can find the codes that I have written in [this github repository](https://github.com/simulkade/peteng). Here, I only call the codes and compare the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# load the input parameters and the functions\n",
    "using Roots, PyPlot, Dierckx, JFVM\n",
    "import JSON, JLD\n",
    "include(\"../functions/rel_perms_real.jl\")\n",
    "include(\"forced_imbibition_corey.jl\")\n",
    "include(\"frac_flow_funcs.jl\")\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The input parameters are stored in the `input_params_BL.jld` file, that can be loaded by"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Compat.ASCIIString is deprecated, use String instead.\n",
      "  likely near In[4]:1\n",
      "WARNING: Compat.UTF8String is deprecated, use String instead.\n",
      "  likely near In[4]:1\n",
      "WARNING: Compat.ASCIIString is deprecated, use String instead.\n",
      "  likely near In[4]:1\n",
      "in jldatatype at /home/ali/.julia/v0.6/JLD/src/jld_types.jl\n",
      "WARNING: Compat.UTF8String is deprecated, use String instead.\n",
      "  likely near In[4]:1\n",
      "in jldatatype at /home/ali/.julia/v0.6/JLD/src/jld_types.jl\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "14-element Array{Symbol,1}:\n",
       " :L_core  \n",
       " :kro0    \n",
       " :krw0    \n",
       " :mu_oil  \n",
       " :mu_water\n",
       " :no      \n",
       " :nw      \n",
       " :perm_ave\n",
       " :poros   \n",
       " :pv_inj  \n",
       " :sor     \n",
       " :swc     \n",
       " :swi     \n",
       " :u_inj   "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "JLD.@load \"results/input_params_BL.jld\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can run the functions for the analytical and numerical solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# call the functions\n",
    "# numerical solution (finite volume)\n",
    "(t_num, R_num, sw_prf)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj, Nx=50)\n",
    "IJulia.clear_output()\n",
    "\n",
    "# Analytical solution (BL)\n",
    "(xt_shock, sw_shock, xt_prf, sw_prf, t_anal, p_inj, R_anal) = frac_flow_wf(\n",
    "  muw=mu_water, muo=mu_oil, ut=u_inj, phi=poros,\n",
    "  k=perm_ave, swc=swc, sor=sor, kro0=kro0, no=no, \n",
    "  krw0=krw0, nw=nw, sw0=swi, sw_inj=1.0, L=L_core, pv_inj=pv_inj)\n",
    "IJulia.clear_output() # only to clear the output from the previous function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can plot the results and compare the solutions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9aeda1ca50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(t_anal, R_anal, \"o\", t_num, R_num)\n",
    "xlabel(\"time [s]\")\n",
    "ylabel(\"Recovery factor [-]\")\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It seems that the match very well. But if we zoom on the recovery plot close to the water breakthrough time,"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9ac96600d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(t_anal, R_anal, \"o\", t_num, R_num)\n",
    "xlabel(\"time [s]\")\n",
    "ylabel(\"Recovery factor [-]\")\n",
    "axis([25000, 50000, 0.40, 0.5])\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "we can see that there is roughly 1 percent underestimation of the recovery factor by the numerical method. One reason is the numerical diffusion in the upwind scheme that I have used in my numerical solution. With this diffusion, the front is not sharp anymore and the water breakthrough (decrease in the slope of the recovery curve from the linear trend) happens a bit earlier in time. Let's test it by plotting the saturation profiles:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9ac957ee50>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pv_inj2 = 0.3\n",
    "(t_num, R_num, sw_prf_num)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj2, Nx=50)\n",
    "\n",
    "# Analytical solution (BL)\n",
    "(xt_shock, sw_shock, xt_prf, sw_prf, t_anal, p_inj, R_anal) = frac_flow_wf(\n",
    "  muw=mu_water, muo=mu_oil, ut=u_inj, phi=poros,\n",
    "  k=perm_ave, swc=swc, sor=sor, kro0=kro0, no=no, \n",
    "  krw0=krw0, nw=nw, sw0=swi, sw_inj=1.0, L=L_core, pv_inj=pv_inj2)\n",
    "visualizeCells(sw_prf_num)\n",
    "plot(xt_prf*t_anal[end], sw_prf)\n",
    "axis([0, L_core, 0, 1.0])\n",
    "legend([\"Numerical\", \"Analytical\"])\n",
    "xlabel(\"Core length [m]\")\n",
    "ylabel(\"Water saturation [-]\")\n",
    "IJulia.clear_output() # only to clear the output from the previous function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can clearly see that the extra numerical diffusion causes the water front to move faster resulting in an earlier water breakthrough. We can decrease this diffusion by refining the grid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9ac93752d0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(t_num, R_num, sw_prf_num)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj2, Nx=500)\n",
    "visualizeCells(sw_prf_num)\n",
    "plot(xt_prf*t_anal[end], sw_prf)\n",
    "axis([0, L_core, 0, 1.0])\n",
    "legend([\"Numerical\", \"Analytical\"])\n",
    "xlabel(\"Core length [m]\")\n",
    "ylabel(\"Water saturation [-]\")\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can see that the numerical solution is very close to the analytical solution. This must give a better match for the recovery curves as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9ac9369ad0>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# numerical solution (finite volume)\n",
    "(t_num, R_num, sw_prf)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj, Nx=500)\n",
    "\n",
    "# Analytical solution (BL)\n",
    "(xt_shock, sw_shock, xt_prf, sw_prf, t_anal, p_inj, R_anal) = frac_flow_wf(\n",
    "  muw=mu_water, muo=mu_oil, ut=u_inj, phi=poros,\n",
    "  k=perm_ave, swc=swc, sor=sor, kro0=kro0, no=no, \n",
    "  krw0=krw0, nw=nw, sw0=swi, sw_inj=1.0, L=L_core, pv_inj=pv_inj)\n",
    "plot(t_anal, R_anal, \"o\", t_num, R_num)\n",
    "xlabel(\"time [s]\")\n",
    "ylabel(\"Recovery factor [-]\")\n",
    "axis([25000, 50000, 0.40, 0.5])\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## sensitivity analysis\n",
    "Effect of relperm parameters on the total recovery factor, compare to a base case:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "PyPlot.Figure(PyObject <matplotlib.figure.Figure object at 0x7f9ac90c8990>)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n_points = 100\n",
    "R_fact   = zeros(n_points)\n",
    "kro0_range = linspace(kro0, max(kro0, 1.0), n_points)\n",
    "for i = 1:n_points\n",
    "    # Analytical solution (BL)\n",
    "    (xt_shock, sw_shock, xt_prf, sw_prf, t_anal, p_inj, R_anal) = frac_flow_wf(\n",
    "      muw=mu_water, muo=mu_oil, ut=u_inj, phi=poros,\n",
    "      k=perm_ave, swc=swc, sor=sor, kro0=kro0_range[i], no=no, \n",
    "      krw0=krw0, nw=nw, sw0=swi, sw_inj=1.0, L=L_core, pv_inj=pv_inj)\n",
    "    R_fact[i] = R_anal[end]\n",
    "end\n",
    "plot(kro0_range, R_fact, \"-\")\n",
    "xlabel(\"kro0\")\n",
    "ylabel(\"Recovery factor [-]\")\n",
    "# axis([25000, 50000, 0.40, 0.5])\n",
    "IJulia.clear_output()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kro0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "(t_num, R_num, sw_prf)=forced_imb_impes(mu_water, mu_oil, u_inj, \n",
    "    poros, perm_ave, swc, sor, kro0, no,\n",
    "    krw0,nw, swi, 1.0, L_core, pv_inj, Nx=500)"
   ]
  }
 ],
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